Are you looking at the character before "cat" and the character after "cat"?
If you look at the character after "cat" in "category" it is an "e".
"e" is not a valid delimiter so "category" is not a match.

Have you seen any of my posts about looking at the characters before and after where the searched for String is found? I called them the delimiters of the String. The character that is immediately before and the one immediately after the found String.

You need to define all the ways a word can be put in a String. For example:
Starts the String and is followed with a delimiter like space, comma(,), period(.), end of String, etc
Follows a delimiter like a space, comma, etc and is followed by a delimiter or by the end of the String.

Punctuation is not necessary for this assignment, so the period and comma do not need to be dealt with. Aside from that, you've suggested spacing variations, which I have told you multiple times do not solve the problem. You don't seem to understand this.

I have messed around with space delimiters and they don't work. I don't doubt your ability, but I've been programming for three weeks, and your cryptic suggestions are not effective. I'm not asking for you to do my assignment for me, but I am stumped at figuring out how to figure this out. Is it an issue of using a method other than indexOf?

Why does this censor everything as profanity? When I test n1, n2, and n3 by themselves, they return false values when I type "hello there," and true for cat and its spacing variants. So how come my if statements get triggered when I type "hello there"?

I know you said to us length, charAt, and substrings, but this contentEquals method seems like it could work.

The substring in my method will get me the entire string. This is where I get stuck. If I do tests for length, the end up not working if cat is not the last word. I get run time errors with charAt when cat ends a sentence. I can truncate a word like category into cat, but that does not help me. I also tried testing my substrings against contentEquals, but that didn't work either. What can I do with substrings that will allow me to test for differences?

The length you are interested in is that of cat
You want to look at the character in front of or following cat.
Take a piece of paper and write down several sentences with "cat" in it.
Then write under each character in the sentence its position in the sentence starting at 0.
Then consider what indexOf() returns and where the character after "cat" is relative to the value returned by indexOf(). It should be exacty the length of cat (3) characters later.

Most of the problems you describe are because you haven't used a piece of paper and pencil to work out where a String is and what index values will work relative to that location.
For example if indexOf() returns a 0, there won't be a character in front of it.